by
Stewart, James; Redlin, Lothar; Watson, Saleem

Answer

$x\approx 1.68$

Work Step by Step

Subtract $1$ on both sides of the equation to obtain:
$\ln{(2x-3)}=-1$
RECALL:
$\ln{x} = y \longrightarrow e^y=x$
Use the rule above to obtain:
$e^{-1} = 2x-3$
Use the rule $a^{-m} = \dfrac{1}{a^m}$ to obtain:
$\dfrac{1}{e} = 2x-3$
Add $3$ on both sides of the equation to obtain:
$\dfrac{1}{e} + 3 = 2x$
Divide $2$ on both sides of the equation to obtain:
$\dfrac{\frac{1}{e} + 3}{2}=x$
Use a calculator to obtain:
$x\approx 1.68$